Atmospheric Measurement Techniques Minimizing light absorption measurement artifacts of the Aethalometer : evaluation of five correction algorithms

The aerosol light absorption coefficient is an essential parameter involved in atmospheric radiation budget calculations. The Aethalometer (AE) has the great advantage of measuring the aerosol light absorption coefficient at several wavelengths, but the derived absorption coefficients are systematically too high when compared to reference methods. Up to now, four different correction algorithms of the AE absorption coefficients have been proposed by several authors. A new correction scheme based on these previously published methods has been developed, which accounts for the optical properties of the aerosol particles embedded in the filter. All the corrections have been tested on six datasets representing different aerosol types and loadings and include multi-wavelength AE and white-light AE. All the corrections have also been evaluated through comparison with a MultiAngle Absorption Photometer (MAAP) for four datasets lasting between 6 months and five years. The modification of the wavelength dependence by the different corrections is analyzed in detail. The performances and the limits of all AE corrections are determined and recommendations are given. Correspondence to: M. Collaud Coen (martine.collaud@meteoswiss.ch)


Introduction
The single scattering albedo ω 0 and the extinction Ångström exponent of atmospheric aerosol particles are needed in models calculating aerosol radiative forcing.These parameters can be determined from concomitant multi-wavelength measurements of aerosol scattering and absorption coefficients.Instruments and methods to measure the light absorption by atmospheric particles have been described in detail elsewhere (Bohren and Huffman, 1983;Horvath, 1993;Heintzenberg et al., 1997;Moosmüller et al., 1997;Bond and Bergstrom, 2006).Among the direct measurement methods, filter-based instruments have been widely used both at ground sites and on airborne platforms due to their ease of operation.However, most of the filter-based absorption techniques, which determine the aerosol absorption coefficient from the attenuation of light passing through an aerosol-laden filter, suffer from various systematic errors that need to be corrected (Liousse et al., 1993;Petzold et al., 1997;Bond et al., 1999): firstly, attenuation is enhanced by multiple scattering by the filter fibers which increases the optical path (multiple scattering correction); secondly, light attenuation is further enhanced due to scattering of aerosols embedded in the filter (scattering correction); and thirdly, attenuation is gradually Published by Copernicus Publications on behalf of the European Geosciences Union.
increased by the light absorbing particles accumulating in the filter thus reducing the optical path for a loaded filter (filterloading correction).
The most frequently used filter-based commercial instruments to measure real-time black carbon (BC) mass concentrations are the Aethalometer (AE) and the Particle Soot Absorption Photometer (PSAP).The multi-wavelength AE measures at seven wavelengths covering the ultra-violet to the near-infrared wavelength range (the AE-31 measures in the range from λ=370 to 950 nm), the multi-wavelength PSAP has only recently become commercially available and measures at three wavelengths (λ=467 to 660 nm).The absorption data from both instruments need to be corrected for the above mentioned artifacts in the filter matrix and these corrections require concomitant scattering measurements.In contrast to the AE and PSAP, the more recently developed Multi-Angle Absorption Photometer (MAAP) detects not only the transmitted, but also the backscattered light at two angles to resolve the influence of light-scattering aerosol components on the angular distribution of the backscattered radiation.The absorption coefficient at λ=630 nm is thereafter obtained from a radiative transfer scheme (Petzold and Schönlinner, 2004;Petzold et al., 2005).This technique treats the multiple scattering in the filter and the scattering effect of the particles embedded on the filter.Hence, the MAAP instrument does not use any empirically determined, aerosol-related correction factors.The instrumental artifacts are reduced for the MAAP in comparison with AE or PSAP, so that the absorption coefficients measured with a MAAP should be closer to the true ones.Even if the MAAP is not an absolute reference method, it is however used as a reference for AE in this paper.
Various correction schemes have been published for the PSAP (Bond et al., 1999;Virkkula et al., 2005a) taking into account the above mentioned artifacts, and particularly the scattering correction.Similarly, AE correction methods presented in the literature also take these effects into account (Weingartner et al., 2003;Arnott et al, 2005;Schmid et al., 2006;Virkkula et al., 2007).
Using the above mentioned correction methods, high instrument correlation but with highly variable regression slopes were found for intercomparison measurements with various absorption instruments both in the laboratory and under atmospheric conditions (Arnott et al., 2005;Saathoff et al., 2003;Schmid et al., 2006;Wallace, 2005;Rice, 2004;Petzold et al., 2005;Virkkula et al., 2005a, b;Schnaiter et al., 2005;Park et al., 2006;Slowik et al., 2007).For example, the intercomparison of continuously operated Aethalometers, MAAPs and Photoacoustic spectrometers (PAS) at the Fresno Supersite (Park et al., 2006) resulted in regression slopes between 0.2 and 2. The intercomparison also pointed out differences between winter and summer measurements indicating that the aerosol composition also plays an important role for instrument correlation.
It is widely accepted (Arnott et al., 2005;Schmid et al, 2006;Rice, 2004) that the uncorrected AE measures too high absorption coefficients.Weingartner et al. (2003), Arnott et al. (2005) and Schmid et al. (2006) published AE corrections, taking into account either results of chamber experiments involving extinction and scattering coefficient measurements or comparison with a PAS.The ability to correct the AE and/or PSAP for all of the above mentioned instrumental artifacts is important: firstly, to derive climatically important aerosol parameters more accurately from a simple instrument; secondly, to take advantage of already existing long-term data sets (such as the 13-year AE dataset from the Jungfraujoch (JFJ), or the 15-year AE dataset from Mace Head (MHD, see Junker et al., 2006)); and thirdly, to perform multi-wavelength measurements providing spectral information on absorption and single scattering albedo, which is not yet available from more reliable instruments.
Two new AE corrections are developed in this paper, using already published AE corrections schemes.These new corrections as well as all the previously published ones were tested on six datasets from different sites, of which four also included a MAAP (Table 1).The analyzed absorption coefficients include aerosol measured in the Alps (Jungfraujoch, Hohenpeissenberg, HOP), in a flat region near populated and industrialized areas (Cabauw, CAB), at a coastal site (Mace Head), on a pasture site affected by biomass burning (Amazon Basin, AMA) and in a city (Thessaloniki, THE).Therefore these sites represent free tropospheric, continental, maritime, biomass burning and heavily polluted environments and are characterized by a annual mean single scattering albedo (ω 0 ) between 0.65 and 0.90 (at λ=660-840 nm).Comparisons with a MAAP have been performed on datasets lasting between six months and five years, so that the correlation between both absorption measurements can be established on real atmospheric aerosols during a time period long enough to study the performance of MAAP and AE instruments and associated corrections in long-term monitoring programs.

Measurement sites and instrumentation
Table 1 gives the main characteristics of the used datasets.All measurement sites use the same Nephelometer and MAAP types.The three kinds of AE (AE-31, AE-16 and AE-10, AE-30 being the prototype of AE-31) work with similar filter tapes (Pallflex Q250F) consisting of non-woven polyester backed quartz filter material.The main difference in the instrumentation concerns the inlet types that sample different aerosol size fractions (PM 1 , PM 10 or TSP) at different relative humidities (from dry to ambient conditions) leading to different aerosol patterns.However, at each measuring site, all three used instruments (AE, MAAP and Nephelometer) sampled aerosol from the same inlet, so that comparisons are always performed for the same size fraction and relative humidity.The scattering and backscattering coefficients of all stations were measured by Integrating Nephelometers and corrected for the truncation error and for the non-idealities in the angular intensity distribution of the light inside the instrument according to Anderson and Ogren (1998) and Nessler et al. (2005).All the data were aggregated to hourly means.
The multi-wavelength AE's cover the 370-950 nm wavelength range, and the white-light AE's have a broad spectral range from 500 nm to 1100 nm with a peak sensitivity in the near IR at about 840 nm (Weingartner et al., 2003).All the AE's undergo a filter-preconditioning cycle after each tape change that exposes the filter to sampled air before the measurement starts.In rack mounted Aethalometers (AE16, AE21, AE22, AE31) the sample flows through the filter tape for a part of the preconditioning cycle only (about 3 min), and the flow is diverted through a by-pass cartridge filter during most of the preconditioning cycle (G. Mocnik, Aerosol d.o.o., Magee Scientific, personal communication, 2009).This preconditioning cycle can modify the zero point of the light intensity I 0 (see Eq. 1 below) and consequently the attenuation ATN.The ATN modification will change the filter loading correction and induce a lower calibration constant C ref for the multiple scattering correction that was estimated to less than 5% for the studied datasets.As also stated in Arnott et al. (2005), this is normally not an issue for ambient measurements as reported in this study, but it could be an issue when sampling from highly polluted sources.A better quantification of this effect is however not possible since the shift of the zero point of the filter transmittance is presently not known.

Aethalometer corrections
All the already published corrections are summarized in this section and the mentioned equations report only the final applied corrections.To enable a better comprehension of all corrections proposed, Table 2 lists all the used parameters, their units, a brief description and the corresponding parameters used in the previously published correction schemes, and Fig. 1 schematically describes the new correction scheme.In the following, some formal definitions are first given.The light attenuation (ATN) through the aerosol-laden section of a filter spot is defined as where I 0 is the intensity of light passing through a pristine portion of the filter and I the intensity passing through the loaded filter.The particles embedded in the filter during a time interval t will increase ATN, so that the nth measure of the aerosol attenuation coefficient (b ATN,n ) of the filtered aerosol particles is obtained from where A is the area of the sample spot and V the volumetric flow rate.The corrections discussed below are then applied to infer the true aerosol absorption coefficient b abs,n of airborne particles from b ATN,n .
Both the absorption Ångström exponent åabs and the scattering Ångström exponent åscat , which refer to the wavelength dependence of the respective coefficients, were determined by fitting the measured absorption or scattering coefficients with a wavelength power-law dependence (b ∼ λ − å ).These Ångström exponents were used to calculate coeffi-cients at other wavelengths, such as the absorption coefficient at λ=630 nm to allow comparison with the MAAP.Weingartner et al. (2003) proposed an empirical correction R W for the attenuation effect due to the filter-loading and determined the calibration constant C ref for different aerosol types produced in the AIDA aerosol chamber (at FZ Karlsruhe, Germany) to correct for the multiple scattering in the filter matrix.The resulting nth absorption coefficient b abs,n is given by:

The Weingartner correction
where C ref is determined by first correcting b ATN for the filter-loading correction and then comparing it with the absorption coefficient measured simultaneously with a reference instrument (b abs,ref ).Since the Weingartner filterloading correction R W takes ATN=10% as a reference point, C ref relates in this case to ATN=10%: A parameter f (λ) is introduced which characterizes the slope between b ATN,n and ln(ATN n ) and parameterizes the filterloading correction R W .A clear dependence of f on 1−ω 0 was also observed for pure, internally and externally mixed diesel soot particles, which leads to the following quasilinear relation where m is nearly constant (0.87 to 0.85) for λ=470 to 660 nm.The Weingartner correction parameter R W can depend on the light wavelength, but C ref does not.Therefore, a constant C ref value over the wide spectral range (370-950 nm) was chosen.Weingartner et al. (2003) also determined f values for different aerosol types.In this paper, R W will always correspond to the Weingartner correction with fixed f values chosen for each dataset depending on the aerosol type, as it is presently applied by most users, so that the R W correction does not need concomitant b scat measurements once f has been determined.It is evident from Eqs. 3 through 5 that if ω 0 =1, both f and R W are equal to unity.Since the aerosol measured at the high alpine site JFJ was aged aerosol with ω 0 values mostly close to unity, R W can be taken as unity.Arnott et al. (2005) proposed a theoretically well documented correction, which includes an explicit scattering correction similarly to the correction commonly applied to the PSAP (Bond et al., 1999).The form of this scattering correction (−α • b scat ) was deduced from the non-zero b ATN measured by an AE with a purely scattering aerosol.The scattering coefficient b scat weighted by the α values was therefore subtracted from b ATN to correct for the scattering artifact (Eq.6).The Arnott filter-loading correction R A was derived from multiple scattering theory, which shows that the exponential behavior of light absorption in the strong multiple scattering limit scales as the square root of the total absorption optical depth.The corrected b abs,n is given by :

The Arnott correction
where n, V , t, and A were introduced in Eq. 2, and τ a,f x (λ) is the filter absorption optical depth for the filter fraction x that has particles embedded in it, and C ref is obtained by comparison between AE and PAS absorption coefficients.τ a,f x (λ) and C ref (λ) were determined from kerosene soot measurements during the Reno Aerosol Optics Experiment, under the condition that b abs (λ), when extrapolated to λ=532 nm with åabs =1, were all equal to PAS measurements at λ=532 nm.In this Arnott correction, all the reported calibration constants depend on the wavelength of the light.Six weeks of ambient measurements at an urban site allowed testing of the proposed correction, which showed that different values of the above described parameters are needed for ambient and laboratory generated aerosol.Arnott et al. (2005) also hypothesized that the variation in these parameters is related to the AE pre-conditioning cycles that blackened the filters before the measurement began.

The Schmid correction
The corrected b abs measured either by an AE or a PSAP were compared to the b abs measured by a PAS at λ=532 nm for some days of measurements in AMA, leading to high correlations and ratios between AE and PAS b abs of between 0.94 and 1.03.

Virkkula filter-loading correction
Virkkula et al. ( 2007) proposed a filter-loading correction R V very close to that of the PSAP, assuming that the three last values measured on the filter spot i and the three first values measured on the next filter spot i+1 should be equal, and that the values measured on lightly loaded filters are the closest to the real concentration: where t i,last is the time of the last measurement on the filter spot i and t i+1,first is the time of the first measurement on the next filter spot i + 1.A k i value is therefore determined for each filter spot and applied to all n measurements on the ith filter spot.The correction was validated by a comparison with simultaneous aerosol volume concentration measurements at three sites with different aerosol types.Virkkula et al. (2007) chose to set the scattering correction to zero, since a lot of AE users do not have concomitant scattering measurements.In addition, they did not introduce a multiple scattering correction.Henceforth, the Virkkula correction will be considered as a filter-loading correction only and not as a total correction of the attenuation coefficient, since the multiple scattering correction is not negligible as will be shown below.

The new correction
The necessity of a further development of the above described corrections became obvious when the corrections were applied to the JFJ dataset (see Sects. 3 and 4).Firstly, the Weingartner filter-loading correction R W results in 1/R W <1 for ATN<10%.Considering that a pristine filter should produce no artifact, 1/R W should be equal to 1 for ATN=0.The subtraction of ln(10%) was therefore removed for the new filter-loading correction.Weingartner et al. (2003) found a linear relationship between b ATN and ln(ATN), which leads to a m value (Eq.5) independent of the wavelength.Recent experiments with aged diesel soot showed a linear relationship between b ATN and ATN (Steiger, 2008).Investigations of the JFJ and THE datasets show that the regressions between b ATN and ATN are statistically better than between b ATN and ln(ATN).The direct proportionality is therefore chosen for the modified Weingartner filter-loading correction (Eq.13).A new m value was consequently calculated similarly to that of Weingartner et al. (2003) and with the same datasets from the AIDA chamber experiment but by fitting a linear relationship between b ATN and ATN.This m value has a mean value m=0.74 when averaged over the experiments and the wavelengths, but is wavelength dependent.It was verified for all datasets that a change of the m value induces a change in the calculated C ref but insignificant changes in the final b abs values.The new filter-loading correction is: where ATN is given in %, ω0,s,n is the mean of the n single scattering albedo measured since the filter spot change, where the subscript s indicates that the mean optical properties of the aerosol particles embedded in the filter spot and not only of the nth measurement are taken into account.
Secondly, the new corrections take explicitly into account the fact that the AE measures a non-zero b abs when loaded with non-absorbing aerosol.Either the Arnott or the Schmid scattering correction schemes can be applied.Both corrections use the Arnott α(λ) parameters to weight the scattering correction.Following the Arnott assumption of α being constant for a defined λ, the ratio b abs /b scat for nonabsorbing aerosols should be constant, independently of the value of b scat .The 2007 EUSAAR intercomparison campaign in Leipzig showed however that the ratio between the absorption and scattering optical depth increased with decreasing scattering optical depth for all filter-based instruments (PSAP, MAAP and AE) (Müller et al., 2008).The scattering coefficient and its wavelength dependence (Eq.8) should therefore match the measured aerosol and not the ammonium sulfate experiment involving high ω 0 and high åscat ( åscat,non−abs =3).The Arnott β scat,non−abs and åscat,non−abs constants have therefore to correspond to β scat and åscat of the aerosol particles embedded in the filter spot.Therefore, the main modification introduced by the new correction is that the constant β scat,non−abs and åscat,non−abs of Eq. 8 are replaced by a mean scattering coefficient βscat,s,n and a mean scattering Ångström exponent āscat,s,n of the total aerosol load in the filter spot.The power-law regression between b ATN and b scat for non-absorbing aerosols (Eq.9) can on the other hand be considered to be universal, so that the constants c and d can be taken from Arnott et al. (2005).This new α new,n (λ) (see Eq. 15 below) allows one to take the real scattering properties of the measured aerosol into account and is therefore applied to both the Arnott and Schmid scattering correction schemes, leading to two new corrections.Similarly, instead of using b scat,n or ω 0,n measured simultaneously with the nth absorption measurement b abs,n since a filter spot change, the mean scattering coefficient bscat,s,n or the mean single scattering albedo ω0,s,n of the total aerosol loading in the filter spot are used for the Arnott scattering and for the Schmid scattering corrections, respectively.
Finally the new AE correction is described in Fig. 1 and by Eqs.14a or 14b depending if the Arnott or the Schmid scattering correction is applied: The wavelength dependent ω 0 (λ) (Eq.16) is obtained from ω 0,ref that can be calculated with the scattering coefficient taken at one of the AE wavelengths λ ref and the first estimation of b abs = b ATN /SG (Schmid et al., 2006), where SG is the mass specific attenuation cross-section proposed by the manufacturer (14625/λ [m 2 g −1 ], λ in [nm]).It was verified with the JFJ and THE datasets that the choice of the initial wavelength λ ref is not important for the final result:     The filter-loading artifact can be clearly visualized after a filter change in a distinct step in b ATN during chamber studies, when the aerosol type and concentration remains fairly constant.In an ambient environment however, steps in b ATN are not only due to the filter-loading artifact but also due to the natural variability of the aerosol properties.The efficacy of the four filter-loading corrections to smooth steps in b ATN due to the filter-loading artifact was tested on the THE and JFJ datasets, leading to no significant differences between the filter-loading corrections.
The averaged effect of the filter-loading correction is plotted in Fig. 3 as a function of ATN for the various datasets.At ATN=60% the filter loading correction increases b abs by 7 to 25% depending on the station.The greatest filter-loading corrections are found for MHD and for the most polluted environments (THE, CAB).having however the smallest variability with ATN for the smallest ATN.At MHD, the Weingartner and Arnott corrections are the flattest ones, the new correction becoming too large at high ATN.

The multiple scattering correction
For the evaluation of C ref of the multi-wavelength AE, the wavelength of λ=660 nm, which is nearest to the MAAP wavelength (λ=630 m), was chosen.The comparison of the AE and MAAP for the four datasets leads to average C ref values between 2.9 and 4.3 ( According to the correction schemes, the multiple scattering artifact should depend only on the filter properties and not on the embedded aerosol.However, the calculated C ref is not always constant, even at the same station.This variation of C ref could be caused by semi-volatile organic compounds (VOCs) and water vapor condensing on the filter fibers (Weingartner et al., 2003) or to other similar phenomena such as organic particles emitted from low-temperature biomass burning that have a liquid, bead-like appearance when collected on fibrous filters (Subramenian et al., 2007).Firstly, the scattering of the filter fibers can be enhanced by these compounds, leading to a longer optical path length; secondly, the scattering phase function can also be modified leading to a modification of the mean filter reflectance; thirdly, the sticking coefficient (probability to stick on a surface) of the aerosol on the fiber and the possible change of the inter-fiber spacing can change the depth of aerosol deposition in the filter, leading to a change in its optical properties.The experimental setup used in this study does not allow us to further investigate these potential influences.

The scattering correction
The loading of the filter with scattering aerosol leads to two different artifacts: the aerosol particles scatter light in all directions, leading firstly to an increase of backscattered light and consequently to an apparent greater reflectance of the filter, and secondly to an increased light optical path and consequently to a higher probability of encountering an embedded absorbing particle.Due to its form, the applied scattering correction (subtraction of an amount proportional to the scattering coefficient) clearly corrects for an increase in the reflectance.The reflectance depends on the aerosol asymmetry parameter, which is lower for longer wavelengths, so that the proportionality factor α should increase with increasing wavelength.The second scattering artifact, as described above, leads to a higher probability of encountering an embedded particle, which is presently not compensated by any correction.The MAAP measurement technique does not correct for this second artifact either, but shows close agreement with a reference absorption measurement through the difference between light extinction and scattering (Petzold et al., 2005).This second scattering effect is therefore probably not very pronounced.
Contrary to the Arnott scattering correction, but according to recent results (Müller et al., 2008) (see Sect. 2.2.5), the new correction introduces an α new (λ) that depends on βscat and āscat (Eq.15). Figure 6a shows α new at λ=660 nm as a function of b scat for the JFJ, CAB, AMA and THE datasets.α new (λ) is lower than about 0.08 for the CAB, AMA and THE datasets.When applied to the JFJ dataset, α new (λ) ranges between 0 and 0.20, but the great majority of α new (λ) values are smaller than 0.1.As expected from the wavelength dependence of the asymmetry parameter, α new is greater at longer wavelengths.Since åscat at AMA and THE are always near 2 (standard deviation <0.15 for the two stations), α new clearly increases with decreasing b scat .åscat has a lower mean for the JFJ and CAB datasets (1.64±1.25 and 1.56±0.72,respectively), and is much more variable, particularly at the JFJ, due firstly to the longer dataset and secondly to the presence of aged accumulation mode aerosol (Weingartner et al., 1999), which are coarser and lead to low åscat and sometimes even to negative åscat in presence of mineral particles.α new is therefore not always increasing with b scat , but tends towards zero for very low åscat .
Figure 6b shows the C scat dependence on ω 0 for the JFJ, CAB, AMA and THE datasets.As can be deduced from Eq. 14b, C scat increases with increasing ω 0 .While the C scat dependence on ω 0 is well defined for the high aerosol loading at Thessaloniki, it becomes less sharp at lower aerosol concentrations, particularly at the JFJ, due firstly to a greater uncertainty in the measurement of very low b abs and b scat and secondly to a broader range of α new values (see Fig. 5a).C scat maximum values can be equal to 2 for ω 0 near one at the JFJ, but remains normally below 0.5 for most values of ω 0 <0.95.The C scat correction is usually greater at longer wavelengths, but inversion of this wavelength dependence is also observed.
Figure 3 shows that the new scattering correction decreases b abs on average by 2 to 12% depending on the station.The greatest scattering correction is obtained for the high altitude stations (JFJ, HOP) where aged aerosols are measured.Since the new scattering correction takes into account the mean scattering of all the aerosol embedded into the filter, this correction tends to be more constant with higher filter loading.

Applicability of the AE corrections
The very low aerosol concentrations, particularly at the JFJ and MHD, induce some instrumental difficulties.Due to the fact that the measurements result from the difference between the last and the last before the last measured light attenuation through a loaded filter, very low concentrations sometimes induce negative b abs due to electronic noise in the raw signals (Petzold and Schönlinner, 2004).Even if negative b abs are not real, these values have to be kept, because they are necessary to avoid a bias in the calculated averages.The amount of negative b abs can be lowered by use of larger flow rates or by longer integrating times.Long-term monitoring sites may however have constraints in not allowing variable integrating times.In addition, long integrating times may induce a loss of information such as, for example, diurnal cycles.Correction algorithms that can be applied to negative values are therefore necessary.
Since the Weingartner correction consists of a simple multiplication with constant factors, it can be applied to the negative values of b abs , it does not create new negative values as other algorithms do (see below), and has no impact on åabs (the difference between the measured and the Weingartner corrected åabs is less than 0.01%), as long as f is taken as a constant for a given dataset.
The Arnott correction is able to treat negative values of b abs .Due to the subtraction of the scattering correction, the Arnott correction often creates new negative values of b abs .This artifact is found to be small for the shorter wavelengths (2.9% and 0.3% at λ=370 nm), but the created negative values reach up to 9.6% and 3.4% at λ=950 nm at JFJ and CAB, respectively.The given constants C ref (λ) also yield too high values of b abs .Finally, the Arnott correction has a broad impact on åabs .As can be seen in Fig. 7, the Arnott correction produces values of åabs that are on average 25% higher than the initially measured ones for both datasets.
The Schmid correction depends on ω 0 ; negative values of b abs lead to ω 0 values greater than 1 and therefore to negative C scat values for the scattering correction.The use of åabs to calculate ω 0 prevents its application to negative b abs .This produces new missing values of b abs (2.3% and 0.9% at JFJ and CAB, respectively) and a few new negative values of b abs (< 0.1% for both datasets).The absorption wavelength dependence is also clearly modified, leading to åabs on average 10-15% higher than the initially measured ones (Fig. 6) for both datasets.
The new AE corrections cannot be used for negative b abs , similarly to the Schmid correction.They therefore generate missing values unless åabs values are averaged in the case of negative b abs .If the new correction similar to the Arnott method (Eq.14a) is used, new negative b abs values are generated (2.1% and <0.1% at λ=370 nm and 2.8% and <0.1% at λ=950 nm at JFJ and CAB, respectively) due to the scattering correction subtraction, which is rather less than use of the Arnott correction at high wavelength values.It also introduces more outliers than the new method, similar to the Schmid method.Finally this new correction mainly preserves åabs (Fig. 6) with 58% and 46% of the exponents remaining constant, with 18% and 42% of the exponents having a difference of only 5%, and 7% and finally 1% of the exponents having a 10% difference from the initially measured exponent at JFJ and CAB, respectively.

Correlation of b abs values derived from AE and MAAP
As already stated in the introduction, the MAAP is not an absolute reference method for the absorption coefficient, but it has reduced the AE artifacts by using a sophisticated radiative transfer scheme.Due to its better measuring procedure and to its availability at various measurement sites for several years, the MAAP will be taken in the following as a reference to evaluate the AE corrections.The slopes of the linear regression between the corrected and the MAAP b abs values are reported in Fig. 8 for each month of simultaneous AE and MAAP measurements at the four stations.The averages of the monthly slopes with their standard deviations are given in Table 5.As already mentioned the Arnott correction produces a lot of outliers and has consequently very large mean slopes and is therefore not reported in Fig. 8.As can be seen in Table 5, the new correction like the Arnott and like the Schmid methods both lead to very similar results for all the stations but for JFJ, so that only the new correction like the Schmid method is reported in Fig. 7. Finally, the errors on the slope determination are always far smaller than the slope fluctuation between months, so that they have not been reported for clarity purposes.At the JFJ, the Weingartner correction leads to higher slopes and the Schmid correction to lower slopes than the new correction.At CAB and MHD, similar slopes are found for the Weingartner, the Schmid and the new corrections.At HOP the Weingartner correction leads to the slope nearest to Monthly slopes between the MAAP b abs output and the b abs measured by the MAAP in transmission only (thus using the MAAP in a similar way as the AE, i.e. without the backscattering measurements and the radiative transfer scheme, and then treated similarly to AE measurements), are also plotted in Fig. 8 (black dashed line) for the JFJ dataset.Some features such as the slope increase at the end of 2006 followed by a sharp decrease at the beginning of 2007 are also present.The variability of the monthly slopes as a function of time is therefore not only due to AE instrumental non-idealities, but also due to variations in aerosol properties.Parts of this variability might also be attributed to the condensation of VOCs, water vapor or liquid organic particles as described above.Since Arnott et al. (2005) give a prediction for a scattering correction based on aerosol scattering and asymmetry parameters, some unsuccessful attempts were performed to weight the scattering correction with the asymmetry parameters.It was also checked that monthly slopes are not correlated with the asymmetry parameter or with ω 0 .
To evaluate the influence of the filter-loading, the scattering and the multiple scattering corrections individually, the new correction was applied to the four datasets while removing successively the different components of the correction.It was found that less than three percents of the total correction is due to the filter-loading correction R, which was expected due to the very low mean values of 1/R (Table 3).The greatest part of the correction is due to the multiple scattering correction, so that the C ref determination is the most important one to ensure a slope near unity when compared with a reference method.The difference between the Weingartner, the Schmid and the new corrections can be mainly attributed to the scattering correction.For all the four stations, the scattering correction does not have a great impact on the slope between AE and MAAP b abs .Even if the multiple scattering correction is the largest one (150% to 330% depending on C ref ) to correct for the too high b abs value measured by AE, the filter-loading and the scattering corrections remain necessary since they minimize real measurable artifacts and can modify b abs by up to 25% on average (see Fig. 3).

Criteria for a good correction
Before recommendations are formulated on the best way to correct the AE data, criteria for a good correction procedure should be stated.Firstly, the correction has to take into account all known artifacts occurring during measurements.Secondly, the correction should be applicable to all kind of datasets.Thirdly, the correction should introduce few outliers, or new missing or negative values.Fourthly, the correction should lead to the best b abs correlation with a "true" reference method.Fifthly, the correction should also lead to a real wavelength dependence of the b abs that is real åabs .Finally, the ease of use of the correction may also be a consideration for choosing a correction method.

Modification of the absorption Ångström exponent by AE corrections
The lack of a reference measurement for åabs requires us to develop some considerations on the effects of each part of the correction on the absorption wavelength dependence.Firstly, the light absorption by aerosol loading in a filter decreases the optical path length.Since aerosol light absorption increases with decreasing wavelength, the filter-loading artifact is expected to be larger at shorter wavelengths and will decrease the absorption wavelength dependence.Secondly, the aerosol light scattering increases but the backscattered fraction decreases with decreasing wavelength.This results in a greater scattering coefficient but a lower reflectance at shorter wavelengths.It is therefore difficult to determine if the scattering correction for increased reflectance should modify the absorption wavelength dependence or not, and, in case of modification, if the åabs will be increased or decreased.Thirdly, due to increasing scattering from the particles with decreasing wavelength, the increase of the absorption due to increased probability of encountering an embedded aerosol particle should lead to an increased absorption wavelength dependence.Fourthly, since the filter fibers are non-absorbing and large (typically 1 micrometer for the quartz fiber and 10 micrometer for the cellulose fiber, Arnott et al., 2005), geometric scattering occurs from the cylindrical fibers, so that the multiple scattering correction can be expected in a first approximation to be wavelength independent and to induce no change in the absorption wavelength dependence.Weingartner et al. (2003) concluded similarly.
Considering the effects of all parts of the correction on the absorption wavelength dependence, it is not possible to make precise conclusions on the expected changes of åabs induced by the AE correction.Weingartner et al. (2003) show a high correlation between AE åabs and a reference method (measurement of the difference between extinction and scattering) for "pure" Diesel and Palas soot particles as well as soot particles externally mixed with secondary organic aerosol or ammonium sulfate; a lower correlation was found for coated soot particles.Virkkula et al. (2005a) showed a high agreement between åabs from a 3λ-PSAP calculated with the Virkkula method and a reference value for åabs between 1.0 and 1.3.However Virkkula et al. (2005b) also concluded that the correction algorithm could still be improved regarding the wavelength dependence. A. Petzold (personal communication, 2009) showed that the 3λ-PSAP Virkkula correction (Virkkula et al., 2005b) leads to minor modification of åabs for values around 1 but to up to 2.5 times larger åabs for values around 4 corresponding to desert dust.The wavelength dependence of the PSAP filter transmission is far greater than that of the AE filter, which has a low wavelength dependence (see Fig. 6 in Arnott et al., 2005).Since the reflectance of an AE filter is greater than of a PSAP filter (Arnott et al., 2005), its dependence on the scattering artifact is lower (Lindberg et al., 1999).The discrepancy between real and measured åabs is therefore probably smaller for an AE than for PSAP measurements.Reviewing literature and taking into account all considerations about the modification of the absorption wavelength dependence induced by measurement artifacts, an AE correction that minimizes modifications of åabs is preferred.
Both the Arnott and the Schmid corrections induce important åabs modifications.A finer analysis of these wavelength dependent modifications shows that they are present mostly for low åscat and are greater for low positive åabs .They are in fact due to the wavelength dependence of the scattering correction constants α(λ): since the α wavelength dependence is fixed for both Arnott and Schmid corrections (α ∼ λ +1.3 ), the subtracted amount of the scattering correction increases with increasing wavelength for low åscat .The large åabs increase (Fig. 6) is therefore determined by the scattering properties of both non-absorbing and Diesel-soot aerosols measured by Arnott in a chamber study and cannot be explained by considerations about the wavelength dependence modification due to the scattering correction.The Weingartner correction keeps the measured åabs absolutely unmodified for all aerosol types.The new correction similar to the Arnott or to the Schmid method mainly preserves åabs , inducing a small increase of åabs in some cases, particularly in presence of mineral dust as determined for the JFJ dataset.Since no åabs reference measurements are available to determine the true absorption coefficient wavelength dependence, the new correction probably offers a median solution between no modification and large modifications that are not based on theoretically or experimentally founded reasons.

Evaluation of each AE correction
Taking into account the criteria for a good correction procedure defined in Sect.4.1, Table 6 summarizes the applicability and the performances of each AE correction scheme.
The AE correction proposed by Virkkula et al. (2007) does not take into account all the known artifacts and produces a lot of outliers.It is therefore not recommended to use it on atmospheric aerosol long-term datasets.
The Arnott correction (Arnott et al., 2005) proves to have technical limits mainly due to the generation of new negative b abs values, that are greatly enhanced at lower aerosol concentration and particularly at higher wavelengths.It introduces large ad-hoc modifications of the absorption wavelength dependence, which are not grounded in theory.The Arnott method remains therefore difficult to apply to all atmospheric aerosol datasets.
The empirical Weingartner correction (Weingartner et al., 2003) is easy to use, since it does not directly need b scat measurements, even if an evaluation of ω 0 can influence the filterloading correction.However the determination of the f constant used in the Weingartner filter-loading correction is not clearly defined.It does not modify the åabs and shows a very good agreement with the MAAP.
The Schmid correction (Schmid et al., 2006) needs concomitant scattering coefficient measurements and cannot cope with negative values of b abs .It also introduces artifacts in the absorption wavelength dependence like the Arnott method, but to a lesser extent.It shows good agreement with the MAAP b abs , leading however to smaller slopes than the Weingartner scheme as well as the new corrections for two stations out of the four.
Both new corrections need concomitant scattering coefficient measurements.Similarly to their originals, the new correction like Arnott generates some new negative b abs values and the new correction like Schmid cannot cope with All the corrections apart from the Arnott one lead to pretty good agreements with the MAAP b abs .The small differences in the agreement with the MAAP between the Schmid, the Weingartner and both new corrections leads to the conclusion that C ref is indeed the most important parameter in order to obtain a good agreement with another instrument.The scattering correction, which is achieved differently for the Weingartner, Schmid and the new corrections, has therefore a far lower impact than the multiple scattering correction.The filter-loading and the scattering corrections are however not negligible and remain necessary to correct for the welldocumented corresponding artifacts.The filter-loading correction is more important in the presence of highly polluted environments (low ω 0 ) whereas the scattering correction is the largest in remote stations measuring aged aerosol (high ω 0 ).For stations where no b abs reference measurements are available, Fig. 5 yields an estimate of C ref if ω 0 is known.
The monthly slopes between AE and MAAP b abs vary as a function of time for all datasets with the standard deviations of the monthly slope reaching 8% to 25%.Similar variations are also found as a function of other extensive and intensive aerosol parameters such as b scat , åscat , åabs and ω 0 .The slope between the MAAP b abs calculated by the MAAP software including the backscatter measurement and from the MAAP transmission measurement only (similarly to AE) are also not constant as a function of time (Fig. 7).The inter-comparison of six carbon measurement methods at the Fresno Supersite during a year (Park et al., 2006) also resulted in standard deviations of monthly values ranging between 6% and 19% of the average of all monthly values.Better results are only met for similar instruments such as two AE's.The comparison of b abs measured by different types of instruments seems to depend always on the aerosol properties despite the presently applied corrections algorithms.Lack et al. (2008) showed that there is a correlation between the aerosol organic content (OC), ranged between 0 and 17 µg m −3 , and the ratio between the b abs measured by a PSAP and a PAS.The aerosol OC was measured during two campaigns of 2.5 months duration at the JFJ (Cozic et al., 2007).Since the daily mean OC showed small variations and did not exceed 1.5 µg m −3 at the JFJ, no correlation between the measured OC and the ratio between the AE and MAAP b abs was found in this dataset.However, several results presented in this paper, particularly the monthly slopes presented in Fig. 8, indicate that the variability in aerosol composition is a main clue to the variable slopes between the absorption coefficients measured by the MAAP and AE instruments at the four sites.

Conclusions and recommendations
Corrections developed by Weingartner, Arnott, Schmid and Virkkula have been applied to datasets obtained from four stations with various aerosol types and loadings, two stations having a multi-wavelength AE and two having whitelight AE.Two new corrections based on previously published ones are also presented and are applied to the four datasets as well as to two datasets measured in the Amazon basin and in Thessaloniki.The main modifications introduced by these new corrections are firstly a new parameterization of the scattering correction, which depends on the scattering coefficient and Ångström exponent, and secondly the consideration of the optical properties of all aerosol embedded in the filter for the filter loading and for the scattering corrections.Comparisons with MAAP b abs were performed for all correction schemes and all four datasets.Principal criteria for a sound AE correction scheme were determined as to provide a good agreement with a reference instrument and to preserve åabs , which is an important parameter measured by the multi-wavelength AE.The Arnott correction generates many new negative b abs at low aerosol concentrations, and it does not preserve åabs .The Schmid correction leads to a good agreement with the MAAP, with slopes between AE and MAAP b abs somewhat lower than the other corrections and it does not preserve åabs either.The empirical Weingartner correction does not need the simultaneous b scat measurement; it has no application restriction for lower aerosol concentrations; it has good agreement with MAAP and it induces no modification of åabs .The f constant determining the filter-loading correction is however not well defined.The new correction scheme has also good agreement with MAAP and it mainly preserves åabs allowing however a modification of åabs , for example in the case of mineral dust events.The new correction similar to the Schmid method leads to a better performance than the one similar to the Arnott method.
The results and recommendations for the AE measurements and correction algorithms are summarized as follows: -Measured attenuation values need to be stored in databases, since they are used for all AE corrections.
-Concomitant scattering coefficient measurements are highly recommended, since they are used in all the corrections, and an estimation of the single scattering albedo ω 0 is important in the determination of several correcting constants.
-The determination of the multiple scattering constant C ref is crucial to allow good agreement with MAAP data or other reference instruments' data.The analysis of data from four stations permits a first estimation of C ref as a function of the single scattering albedo ω 0 .Further analyses, particularly at stations with very high BC load, are however recommended prior to determining a universal correlation between C ref and ω 0 .
-The new filter-loading correction R new is the most appropriate algorithm at two stations because it leads to the most constant ratio between AE and MAAP absorption coefficients as a function of ATN.
-Modification of the absorption coefficient wavelength dependence is a very important factor issue for global radiation transfer assessments.Considerations on the wavelength dependence of each AE artifact does not allow to determine if an increase or a decrease of åabs occurs.The use of multi-wavelength reference methods (when available) should resolve this issue.
-If no scattering coefficient measurements are available, the new correction with α new =0, which corresponds to the Weingartner correction apart from the R calculation, or the Weingartner correction are recommended.
-If scattering coefficient measurements are available, the new correction procedure similar to the Schmid method is recommended.
Fig. 1.Description of the sequence of steps to apply the new correction scheme.
scat,non−abs and åscat,non−abs are obtained from measurements of ammonium sulfate aerosol and correspond to the power-law fit of the wavelength dependence of b scat,non−abs : b scat,non−abs = β scat,non−abs • λ − åscat,non−abs (8) c and d are also obtained from the measured non-zero b ATN in the presence of a non-absorbing aerosol and correspond to the relation between b scat,non−abs and b ATN : Schmid et al. (2006) proposed a correction that includes firstly the filter-loading correction R W with constant values of f and the multiple scattering correction C ref developed byWeingartner et al. (2003).Secondly, comparing Arnott and Weingartner methods, they derived a new scattering correction depending on ω 0 and the α(λ) constants derived by Arnott, which replaces the scattering correction introduced by Arnott.Instead of subtracting a part of b scat in the nominator like Arnott, the Schmid scattering correction adds a term C scat to C ref , leading to a correction that includes both the multiple scattering and the scattering corrections in the denominator: similar to Schmid with the new α new,s,n (λ) given byα new,s,n = βd−1 scat,s,n • c • λ − āscat,s,n •(d−1) (15) with d = 0.564 and c = 0.797 • 10 (−6d) = 0.32910 −3 ,b scat [m −1 ]The C ref is determined by comparing the b ATN already corrected for the filter-loading with the new R new correction to b abs,ref measured by a reference instrument, as described in Eq. 4.

Fig. 2 .Figure 2
Fig. 2. 1/R for the four filter-loading corrections as a function of time for about one month measured at the JFJ at λ=370 nm.

Fig. 3 .
Fig.3.Effect of the filter-loading (•) and of the scattering ( ) partial corrections [(total correction -total correction without one partial correction)/total correction] as a function of the attenuation of light through the filter for 5 stations.At MHD and HOP the maximum of the wavelength is found at 840 nm, where λ=370 nm is reported for multi-wavelength AE (JFJ, CAB, THE).For the THE dataset, a C ref =4.26 similar to the one of CAB was applied.

Fig. 4 .
Fig. 4. C ref calculated from b abs corresponding to a defined ATN as a function of ATN for the four filter-loading corrections and for the JFJ, CAB, MHD and HOP datasets as well as for the b abs AE output calculated as recommended by the manufacturer.For JFJ and CAB, b abs at λ=660 nm are represented.For JFJ, the Virkkula filterloading correction leads to too high C ref values varying between 3.7 and 17, and for HOP, the AE b abs calculated as recommended by the manufacturer leads to around 0.6; these extreme values are not shown for clarity purpose.

Fig. 5 .
Fig. 5. C ref as a function of the single scattering albedo ω 0 for the JFJ, CAB, MHD and HOP datasets.For the JFJ and CAB datasets, C ref and ω 0 are also separated between summer (S) and winter (W).

Fig. 6 .
Fig.6.Dependence (a) α new at λ=660 nm as a function of scattering coefficient at λ=550 nm and (b) C scat as a function of ω 0 at λ=660 nm for the four datasets.α new and C scat , were calculated with the new correction scheme and represent the multiplying factor of the scattering correction (Eq.14a), and the scattering correction in Schmid method (Eq.14b), respectively.

Fig. 7 .
Fig. 7. Histogram of the relative change (in percent) of AE derived åabs values using Arnott, Schmid and the new corrections, the method similar to Schmid being represented here.The JFJ and CAB datasets are presented in light and dark colors, respectively.The numbers of cases represented for ±100% correspond to åabs changes equal or greater than ±100%, with values reaching sometimes up to ±200% or greater.

Fig. 8 .
Fig. 8. Monthly regression slopes between the absorption coefficients at λ=630 nm from the MAAP and the AE (interpolated to λ=630 nm) at the four stations for all the different correction schemes as well as between the absorption coefficients given by the MAAP and those measured by the MAAP in transmission only (black dashed line).For all the corrections schemes, the C ref values from Table 4 are applied.The lack of measurements from September 2005 to March 2006 at the JFJ is due to a leak in the MAAP inlet.

Table 1 .
Description of the used datasets, including the measuring sites, the instruments, time periods and brief site characteristics.

Table 2 .
Seinfeld and Pandis (1998)n of the parameters used in this paper as well as the corresponding symbols used in the papers describing the previously published correction schemes.The used nomenclature follows symbols commonly used bySeinfeld and Pandis (1998).
Weingartner et al. (2003)lts of the four R corrections applied to all the datasets.The constant f of the Weingartner 1/R W correction was estimated fromWeingartner et al. (2003), with f =1.025 corresponding to aged mixed aerosols (JFJ, HOP) and f =1.2 for aerosols near pollution sources (THE), while intermediate values off =1.05 and f =1.10 were taken for MHD and CAB, respectively.The form of the Weingartner filter-loading correction results in 1/R W <1 for ATN<10%, which leads to minimal 1/R W values of 0.77<1/R W <0.93 depending on the station and consequently to an increase of b abs measured on lightly loaded filters.For all the analyzed datasets, the maximum of 1/R W amounts to 1.06, whereas the mean of 1/R W varies between 1.01 and 1.03.
abs .The Virkkula filter-loading correction is highly nonstable, leading to large negative and positive 1/R V outliers.Moreover, its wavelength dependence varies.The difficulty of applying the Virkkula correction is due to the natural high

Table 3 .
Use of the scattering coefficient, minimum, maximum and mean of 1/R values, for all four filter-loading corrections and for the four measuring stations.For the Weingartner correction f =1.025, f =1.1, f =1.05, f =1.025, f =1.025 and f =1.2 were taken for JFJ, CAB, MHD, HOP, AMA and THE datasets, respectively.R values were taken at λ=660 nm for multi-wavelength AE (JFJ, CAB, AMA and THE).

Table 4 .
At JFJ and HOP, the new correction leads to the flattest curve between the ratio b ATN,R corrected /b abs,ref MAAP versus ATN, leading to the lowest standard deviations in Table 4.At CAB, the Arnott correction leads to the flattest curve, the new correction www.atmos-meas-tech.net/3/457/2010/Atmos.Meas.Tech., 3, 457-474, 2010

Table 4 .
Mean C ref constants with standard deviations for all four filter-loading corrections for JFJ, CAB, MHD and HOP stations.The correlation with the MAAP was done with λ=660 nm at JFJ and CAB.

Table 4
0 for the four complete datasets (squares) as well as for the JFJ and CAB datasets divided into 2 seasons.A clear correlation between C ref and ω 0 exists, C ref becoming greater for lower ω 0 .Figure5shows C ref for datasets with ω 0 >0.7.Further analysis with other ambient aerosol types, particularly in very polluted environments with lower ω 0 (< 0.7) such as big cities, should enable an extension of the results to a more universal C ref (ω 0 ) curve.It is very important to establish such correlation, since the multiple scattering correction is the most important one to ensure good agreement with a reference b abs as will be discussed later.
ref is clearly higher during the May-July period than for the rest of the dataset, either because of seasonal variation of the aerosol composition or due to a modification of the inlet during March 2008 (see Table1).HOP and MHD have less distinct seasonal cycles.Figure5shows C ref as a function of ω

Table 5 .
Averages and standard deviations of the monthly slopes between MAAP (λ=630 nm) and AE (reported at λ=630 nm) absorption coefficients measured at the four stations for manufacturer estimation and each AE correction.by the new corrections and finally the Schmid correction.At HOP and JFJ, the Weingartner, the Schmid and the new correction similar to Schmid provide similar standard deviations.At MHD, the Weingartner correction leads to the lowest standard deviation of the slopes, and the new correction to greatest ones.At CAB, the Schmid correction and the new correction similar to Schmid have the lowest standard deviations.The new correction similar to Arnott leads sometimes to higher standard deviations due to the presence of outliers.None of the tested AE corrections are able to get rid of some time dependence of the monthly slopes such as the increase from October 2006 to February 2007 at the JFJ or the decrease in April 2008 at CAB and in October 2005 at HOP.

Table 6 .
Evaluation of the applicability and the performance of AE corrections based on the criteria defined under Sect.4.1.